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中文摘要：
本项目研究非线性脉冲微分系统的若干最新课题。重点研究非线性脉冲自治系统的吸引子性态及复杂动力学行为；在时滞与脉冲共存条件下或在具依赖状态脉冲的复杂情形下系统解的基本规律与特性（包括边值问题、稳定性问题、几何理论、渐近性理论等），还重点研究脉冲偏微分系统的振动性。本项目致力于揭示脉冲对系统产生的质的变化，寻找新途径新方法以探究脉冲微分系统超出连续和离散系统范围的本质特性，这无疑有重要理论意义。现代科技各领域中具有脉冲现象的实际问题是大量存在的。譬如神经网络模型、经济模型、管理模型、生态模型等诸多实际问题数学模型往往其本身就是复杂的有脉冲影响的非线性微分系统，并呈现复杂动力学行为。因此本项目关于周期性、稳定性、振动性、分叉、吸引子等重要特性的研究成果都可有效应用于这些实际模型的精细分析。另外本项目成果还可应用于实际问题的脉冲控制与优化。可见本项目研究有着重要应用背景和很强的实用价值。
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期刊论文
A necessary and sufficient condition for the existence of positive solutions of a class of? singular
Multiple? positive solutions for singular m-point boundary-value problems with nonlinearities depend
Positive Solutions of Singular Initial-Boundary Value Problems to Second-Order Functional Differenti
Multiple Positive Solutions via Index Theory for Singular Boundary Value Problems with Derivative De
Nonlinear Boundary Value Problems on Semi-Infinite Intervals using Weighted Spaces: An Upper and Low
Multiple positive solutions of singular second order boundary value problems with derivative depende
Unbounded solutions for singular boundary value problems on the semi-infinite interval:?upper and lo
Global structure of solutions for a class of two-point boundary value problems? involving singular a
On? structure of positive solutions of singular boundary value problems for impulsive differential e
Positive Solutions to Singular Boundary Value Problems with Sign Changing Nonlinearities on the Half
Positive Solutions for Second Order Singular Boundary Value Problems with Derivative Dependence on I
New discrete analogue of neural networks with nonlinear amplification function and its periodic dyna
Multiple positive solutions for superlinear second order singular boundary value problems with deriv
Oscillation of Higher Order Impulsive Differential Equations of Mixed Type with Constant Argument at
Unbounded Positive Solutions for Second Order Singular Boundary Value Problems with Derivative Depen
Multiple positive solutions for singular problems with mixed boundary data and derivative dependence
Multiple positive solutions for singular boundary-value problems with derivative dependence on finit
Positive solutions for singular
three-point boundary-value problems with sign changing nonlinearitie
Positive solutions for singular initial value problems with sign changing nonlinearities depending o
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